add allow_approx option to inv() and inv_sympd()

include/armadillo_bits/op_inv_gen_bones.hpp

@@ -107,16 +107,19 @@ namespace inv_opts
   
   static constexpr uword flag_none         = uword(0       );
   static constexpr uword flag_tiny         = uword(1u <<  0);
-  static constexpr uword flag_likely_sympd = uword(1u <<  1);
-  static constexpr uword flag_no_sympd     = uword(1u <<  2);
+  static constexpr uword flag_allow_approx = uword(1u <<  1);
+  static constexpr uword flag_likely_sympd = uword(1u <<  2);
+  static constexpr uword flag_no_sympd     = uword(1u <<  3);
   
   struct opts_none         : public opts { inline opts_none()         : opts(flag_none        ) {} };
   struct opts_tiny         : public opts { inline opts_tiny()         : opts(flag_tiny        ) {} };
+  struct opts_allow_approx : public opts { inline opts_allow_approx() : opts(flag_allow_approx) {} };
   struct opts_likely_sympd : public opts { inline opts_likely_sympd() : opts(flag_likely_sympd) {} };
   struct opts_no_sympd     : public opts { inline opts_no_sympd()     : opts(flag_no_sympd    ) {} };
   
   static const opts_none         none;
   static const opts_tiny         tiny;
+  static const opts_allow_approx allow_approx;
   static const opts_likely_sympd likely_sympd;
   static const opts_no_sympd     no_sympd;
   }

include/armadillo_bits/op_inv_gen_meat.hpp

@@ -83,22 +83,39 @@ op_inv_gen_full::apply_direct(Mat<typename T1::elem_type>& out, const Base<typen
   arma_extra_debug_sigprint();
   
   typedef typename T1::elem_type eT;
+  typedef typename T1::pod_type   T;
   
   if(has_user_flags == true )  { arma_extra_debug_print("op_inv_gen_full: has_user_flags = true");  }
   if(has_user_flags == false)  { arma_extra_debug_print("op_inv_gen_full: has_user_flags = false"); }
   
   const bool tiny         = has_user_flags && bool(flags & inv_opts::flag_tiny        );
+  const bool allow_approx = has_user_flags && bool(flags & inv_opts::flag_allow_approx);
   const bool likely_sympd = has_user_flags && bool(flags & inv_opts::flag_likely_sympd);
   const bool no_sympd     = has_user_flags && bool(flags & inv_opts::flag_no_sympd    );
   
   arma_extra_debug_print("op_inv_gen_full: enabled flags:");
   
   if(tiny        )  { arma_extra_debug_print("tiny");         }
+  if(allow_approx)  { arma_extra_debug_print("allow_approx"); }
   if(likely_sympd)  { arma_extra_debug_print("likely_sympd"); }
   if(no_sympd    )  { arma_extra_debug_print("no_sympd");     }
   
   arma_debug_check( (no_sympd && likely_sympd), "inv(): options 'no_sympd' and 'likely_sympd' are mutually exclusive" );
   
+  if(allow_approx)
+    {
+    T rcond = T(0);
+    
+    const bool status = op_inv_gen_rcond::apply_direct(out, rcond, expr);
+    
+    if((status == false) || (rcond < auxlib::epsilon_lapack(out)))
+      {
+      Mat<eT> A = expr.get_ref();
+      
+      return op_pinv::apply_gen(out, A, T(0), uword(0));
+      }
+    }
+  
   out = expr.get_ref();
   
   arma_debug_check( (out.is_square() == false), caller_sig, ": given matrix must be square sized" );

include/armadillo_bits/op_inv_spd_meat.hpp

@@ -89,18 +89,34 @@ op_inv_spd_full::apply_direct(Mat<typename T1::elem_type>& out, const Base<typen
   if(has_user_flags == false)  { arma_extra_debug_print("op_inv_spd_full: has_user_flags = false"); }
   
   const bool tiny         = has_user_flags && bool(flags & inv_opts::flag_tiny        );
+  const bool allow_approx = has_user_flags && bool(flags & inv_opts::flag_allow_approx);
   const bool likely_sympd = has_user_flags && bool(flags & inv_opts::flag_likely_sympd);
   const bool no_sympd     = has_user_flags && bool(flags & inv_opts::flag_no_sympd    );
   
   arma_extra_debug_print("op_inv_spd_full: enabled flags:");
   
   if(tiny        )  { arma_extra_debug_print("tiny");         }
+  if(allow_approx)  { arma_extra_debug_print("allow_approx"); }
   if(likely_sympd)  { arma_extra_debug_print("likely_sympd"); }
   if(no_sympd    )  { arma_extra_debug_print("no_sympd");     }
   
   if(likely_sympd)  { arma_debug_warn_level(1, "inv_sympd(): option 'likely_sympd' ignored" ); }
   if(no_sympd)      { arma_debug_warn_level(1, "inv_sympd(): option 'no_sympd' ignored" );     }
   
+  if(allow_approx)
+    {
+    T rcond = T(0);
+    
+    const bool status = op_inv_spd_rcond::apply_direct(out, rcond, expr);
+    
+    if((status == false) || (rcond < auxlib::epsilon_lapack(out)))
+      {
+      const Mat<eT> A = expr.get_ref();
+      
+      return op_pinv::apply_sym(out, A, T(0), uword(0));
+      }
+    }
+  
   out = expr.get_ref();
   
   arma_debug_check( (out.is_square() == false), "inv_sympd(): given matrix must be square sized" );

include/armadillo_bits/op_pinv_meat.hpp

@@ -224,7 +224,7 @@ op_pinv::apply_sym(Mat<eT>& out, const Mat<eT>& A, typename get_pod_type<eT>::re
 
 
 
-  
+
 template<typename eT>
 inline
 bool